Since I've been perusing guitar tabs in the two weeks since I started learning, I can't help but notice that most popular songs don't seem to involve sharped/flatted notes as the root of their chords.
For example, I'll constantly see maj/minor/sus/7/add9 variants of C, A, G, E, D, Em, Bm, etc, but never C♯m or B♭7 or G♯sus2 etc. Never.
Coming from classical piano, where those chords show up constantly, this feels weird to me. Why is this the case? Or have I just not looked hard enough?
Most instuments have key that are easier to play than others. With brass instruments, you'll see lots of pieces with two or three flats; if you go back to your beginner piano literature, you will find that much will be in C/ Am, or in G/ Em, or F / Dm. With the guitar, the "easy" keys are the ones that have open strings (E A D G b e) in their diatonic chords. Other keys force players to use bar chords or capos, you can't use open strings as pedal notes, you can't use open strings in melodies etc. Of course, it's also a matter of genre. Blues and rock tend to stick to the basic stuff. If you're looking for weird chords in unusual keys, look into jazz guitar, or progressive rock.
I'd say you haven't looked hard enough. But in guitar based songs (those originally written for the guitar, or for ensembles that prominently feature the guitar) they're going to be a little less common.
Any instrument has keys that are going to be more comfortable to play in. For the guitar, those are G, D, A, and E - each of those has very finger-friendly open chords. As a result, many guitarist/songwriters are going to gravitate towards those keys.
But some guitar based songs will still use those chords. One of the examples you give for chords you never see is C#m. Check out Bob Dylan's "Lay Lady Lay" and you'll see it.
If you're playing in an ensemble that does music where other instruments are more prominent, the chords are more likely to be those that are friendly to those instruments. If you play much jazz (or any style with horn sections) you'll come across Bb7 chords all the time, because it's the V7 of Eb - a very friendly key for horns and saxes.
Certainly a lot of easier guitar parts are written in keys that make guitar playing easier. That's the point! A lot of studies - Carcassi, etc., are written in keys which allow open strings to be held as pedal notes to accompany other more intricate parts to be played on upper strings.
Thus keys of E, A and D (and their parallel and occasional relative minors) are commonplace. C and G also feature, as any of the open strings on guitar are diatonic to those keys in particular.
There's also, moving away from the classical side, a lot of electric guitar stuff which sounds better using open strings underneath - hence keys of E, A and D being used a lot. Also E♭ and D crop up when guitars are downtuned.
Looking at other music, the majority of it will be in the original key. Which means a lot of jazz could well be in B♭ or E♭, which is where a guitarist will often find himself. I guess at that point in his playing, he'll be well versed in barres or partial chords, and not have to rely on open strings. Having the luxury of a bass player also obviates this! One reason being vibrato isn't that easy to apply to open strings, and playing a single open string in the middle of a phrase sounds different from the others.
So, yes, there's a lot of 'open string' keys - particularly in beginner type guitar music, and also to utilise the fact that open bass string notes give more freedom for the fingers to play elsewhere on the fretboard, but in some genres, it hardly exists. Also, if a song has been 'written' on guitar, there's a good chance it won't be in B♭, E♭, F♯, C♯, et al!
EDIT - I wrote this answer on the premise of keys that guitar music/tabs are written in - but now it appears you're asking about chords whose root notes aren't C,G,D,A,E etc.
There are many chords in songs which have sharps. e.g. C♯ m, G♯m F♯m, which belong to the keys quoted. In fact, all three are diatonic chords in key E - a very common guitar key. So, yes, they will all appear from time to time. True, there won't be as many B♭, E♭ A♭ rooted chords, because they aren't found in keys favoured by a lot of guitarists. However, as earlier in this answer, they will be found in songs in original keys such as those just mentioned. Along with several minors which actually sound simple - Cm, Gm, Fm, but wouldn't be included in beginner guitar songs if possible.
Occasionally I'll look for a guitar tab and when I find it, I discover inaccuracies by the boatload. That leads me to believe that guitar tabs are sometimes compiled by folks with a less than complete understanding of what they are doing, that is to say, a few basics under their belt and they feel ready to submit their contributions. There are more of these types of players in the world than there are the more advanced and more knowledgeable kind. Add to this, the more advanced and knowledgeable players probably spend less time working up tabs to be posted online so the numbers of their tabs are fewer and further between. Classical piano comes from a different perspective where sight reading is stressed and reliance on tabs is rare, so you might not have been exposed to the vulnerabilities of tabs and may be putting more stock in their absolute value than they deserve. That said, I still use them on occasion with the understanding I might have to bring them up to my level as part of the process.
because the guitar's potential is best exploited by arranging for it in keys more natural to the guitar, that means keys up to three sharps such as G, D, and A, or one flat, such as F, and all the relative minor keys of those keys.
It's like any other string instrument: it is best exploited by using keys that use open strings.
However, that doesn't mean that the guitarist is not capable of playing in any other keys. If it's a pro guitarist he should be capable of playing in any keys, and know every key. But hobbyists don't really bother with that level of knowledge.
Also, why are you only looking at popular songs? Popular songs are not often written in difficult keys: that's true for every instrument, not just the guitar. Why are you comparing classical music with popular music? It makes little sense. Popular music doesn't care about using all 24 major and minor keys, popular music is about other things, such as a catchy tune, or rhythm, etc. If you want to find tons of sharps and flats on guitar, look at the scores of 20th century classical composers who wrote for the classical guitar, such as Benjiamin Britten, Luciano Berio, Malcolm Arnold, Castelnuovo-Tedesco, etc. You'll find there all the sharps and flats you want. But comparing your Chopin concert piano etude with a guitar arrangement of a song by Mariah Carey, makes absolutely no sense. Apples and oranges. :)
The guitar's standard tuning is centered around G major.
If you consider the open strings of standard tuning - EADGBE - those tones are used in C, G, and D major. All other keys require a sharp or flat on at least one of the open strings, so you can't use all the open strings in those other keys.
From that point about the open strings, consider that the commonest key changes are a perfect fifth above and below a tonic. If we use G as the tonic, then C is the fifth below and D is the fifth above. G is in the center.
The primary chords (I, IV, & V of those three keys are: C, F, G & G, C, D & D, G, A. Add to those the common minor chords ii and vi and we get: d, a, e, b.
All of those roots are naturals.
Of course other chords could be used. F#dim and C#dim would be obvious ones. But they would be less common.
